You are interested in finding a 90% confidence interval for the average number o

Question

You are interested in finding a 90% confidence interval for the average number of names that people can correctly recall after being introduced to 40 people at a party. Based on past research, you know that the standard deviation for this number is 6.34 names. Suppose you surveyed 55 randomly selected people and found that they correctly remembered an average of 18.16 names. The standard deviation for this group was 4.28 names. Round your answers to two decimal places.

A. The sampling distribution follows a [ Select ] ["Normal", "F", "Chi-square", "t"]    distribution.

B. With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between [ Select ] ["16.93", "15.03", "16.75", "17.88"] and                        [ Select ] ["18.29", "20.84", "19.92", "19.57"] .

C. If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About [ Select ] ["95", "10", "5", "90"] percent of these confidence intervals will contain the true population mean number of names remembered and about [ Select ] ["90", "5", "10", "95"] percent will not contain the true population mean number of names remembered.

Explanation / Answer

A) The sampling distribution follows a "Normal" distribution

B)

here std error of mean =std deviation/(n)1/2 =6.34/(55)1/2 =0.8549

for 90%CI ; z= -/+1.645

hence  90% confidence interval =sample mean -/+ z*std error =16.75 ; 19.57

With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 16.75 and "19.57"

C) If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About  "90" percent of these confidence intervals will contain the true population mean number of names remembered and about "10" percent will not contain the true population mean number of names remembered.

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